Optimal Rent Extraction in Pre-Industrial England and France – Default Risk and Monitoring Costs

n - 1 (a - θ)²

max ∏npv = —— +--+

θ n+ 1   4b

The optimal fee is equal to²⁷

We can now show how the monitoring cost and the default risk affect
the choice of system of rent extraction.

Proposition 1 The higher (lower) the monitoring cost, c, and default
risk, δ, the lower (higher) is the fee θ, i.e., the more is up-front (ex-post)
collection used.

Proof. The derivatives

2(1-C )
■ = - a .....n-1_______< 0

^{dδ 2}(²⅛ - (1+ δ))²
n + 1

and

∂θ∙ = _        n+1^{(1 + δ})       < ₀

∂c at(2(1 - c) + (1 + δ)n+1 )²

prove the proposition. ■

When shaping the rent-extraction system, the CA weighs the costs
and benefits of up-front collection relative to ex-post collection. The
cost of using up-front collection is that the full value of the office cannot
be collected due to the auction mechanism. The cost of using ex-post
payments is that the agent might steal and that it is costly to borrow.

A high monitoring cost, c, generates much theft such that the ex-post
revenues and the amount that can be borrowed are low. Similarly, only a
small amount can be borrowed when the default risk, δ, is high. In both

1 c

²⁷For θ* > 0, it is necessary that 1+δ > _n-t-.

n+1

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